Realizing a programmable complex analog bandpass filter with arithmetic symmetry (the filter transfer function is symmetric around the programmable center frequency .omega..sub.0) is very difficult. Programmability of such a filter means that the characteristics of a physical component of the filter, for example the resistance of a resistor must be controlled. As an example of the difficulties, see citation [1], which describes an analog programmable real filter in which an effective resistance value (which determines the center frequency of the filter) is obtained by controlling the time a resistor is connected or disconnected in the filter.
On the other hand, programmability of digital or time-discrete filter is easy to obtain by varying the filter coefficients. An example is shown in citation [2].
Citation [3] describes an analog filter that is implemented by a cascade of an anti-aliasing filter, an A/D-converter a real digital filter, a D/A converter and an anti-imaging filter. Such a real digital filter is, however, not capable of providing arithmetic symmetry.